Notes on UP-ideals in UP-algebra

A new branch of the logical algebra: UP-algebras

In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...

Notes on Linear Algebra

Notes on Algebra

These notes contain as little theory as possible, and most results are stated without proof. Any introductory book on algebra will contain proofs and put the results in a more general, and more beautiful framework. For example, a book by Childs [C95] covers all the required material without getting too abstract. It also points out the cryptographic applications. By integer, we mean a positive o...

Notes on Abstract Algebra

1 Functions Definition 1.1. Given sets S and T , suppose there is a subset G ⊆ S × T with the following properties: • If (s1, t1) ∈ G and (s2, t2) ∈ G and s1 = s2 then t1 = t2; • For each s ∈ S, there is an element (s, t) ∈ G. Then for each s ∈ S, there is exactly one element α(s) ∈ T so that (s, α(s)) ∈ G. This defines a function α, with domain S and target T , which can be denoted α : S → T ....

Notes on Universal Algebra

These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to “String Topology” and cacti are announced in Section 2.7.